比率依赖捕食模型的Hopf分支（英文）  

Hopf bifurcation of ratio-dependent predator-prey model

作　　者：李波[1] 

机构地区：[1]江苏师范大学数学与统计学院,徐州221116

出　　处：《黑龙江大学自然科学学报》2015年第5期580-585,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11171286)

摘　　要：讨论带扩散的比率依赖捕食模型在齐次Neumann边界条件下的Hopf分支,通过选择适当的分支参数,证明Hopf分支的存在性。当空间区域是区间(0,π)时,利用规范型理论和中心流形定理,得到该系统分支周期解的方向及稳定性的决定条件。Hopf bifurcation of ratio-dependent predator-prey model with diffusion and homogeneous Neumann boundary condition is considered. By choosing an appropriate bifurcation parameter,the existence of Hopf bifurcations at the positive equilibrium is established. When the spatial domain is chosen to be the interval（ 0,π）,conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution is derived by using the normal form theory and the center manifold theorem.

关 键 词：捕食模型 HOPF分支 周期解 稳定性 

分 类 号：O175.2[理学—数学]